Why is it that even among people born in the same year, some of them identify more strongly with an older cohort, some with their own cohort, and some with a younger cohort? If generational membership were only a matter of when you were born, and what the environment was like along each step of your development, we shouldn't see this kind of variation among folks who were born in the same year.
Going solely off of a hunch from personal experience, it could be due to differences in the generational make-up of a person's extended family.
I was born in 1980, part of a late '70s / early '80s cohort that either gets lumped in as the tail-end of Gen X or is given its own tiny designation, Gen Y, between X-ers and Millennials. I've always felt and acted closer to core X-ers than to core Millennials (who to me seem like they come from another planet), although a good fraction of people in my cohort would tilt more toward the Millennial side. We all recognize that we're neither core X-ers nor core Millennials, yet when pushed off of the fence-sitting position, some of us fall closer to an earlier generation and some to a later generation.
Since we spend quite a bit of time socializing with family members, though, perhaps we should look into that source of influence as well. If they're not related to you, much older and much younger people typically are blind to you, and reject hanging out with you if you try to make yourself seen. But blood is thicker than water, and those much older or younger kids will interact with you and pass along their ways in a family setting.
I've only rarely interacted with the extended family on my dad's side, so I'll stick to the maternal side. Although she was born in the mid-'50s, she is unusually young among her three other siblings, who were born in the early, mid, and late '40s — more typical of the parents of core X-ers. My cousins through them are also all older than me: of those I met regularly growing up, one is a late '60s birth, two are early '70s births, and one is a mid-'70s birth. Our grandparents are also more typical of core X-ers, with one born in the mid-1910s and the other in the early '20s.
I would have to ask around, but I suspect the people in my cohort who tilt more toward the Millennial side of the fence have cousins who are more centered around their own age, aunts and uncles centered around their parents' age ('50s births), and grandparents who are Silents (late '20s / early '30s births). That extended family profile is closer to a Millennial's than an X-er's.
Those are the blood relationships, but when you count the affines (those who marry in), you get the same result as long as there aren't wild age differences in dating and marriage. Growing up, I only got to know the girlfriends (and eventual wives) of two of my cousins, but they were both core X-ers (late '60s or early '70s births). And the uncle-by-marriage that I knew well growing up was a Silent.
In short, if you look at my family tree and cover up my birth year, and my parents', it would like a typical Gen X tree. The lateral influences from my cousins (and once they were old enough, their girlfriends and wives), as well as vertical influences from aunts and uncles and grandparents, are more typical of someone born in the early '70s than the early '80s.
Granted, the less time you spend with your extended family growing up, the weaker this effect will be. And people in my cohort had parents who were part of the Me Generation who didn't mind moving away from their siblings and parents, and who expected us to do so as well once we set off for college and whatever career we wanted to pursue. Status was to be more important than extended family cohesion.
But some of us didn't grow up so isolated from our extended families. My mother's sister and her husband lived only a few blocks away from us when I was in elementary school, and that was a second home for me and my brothers. By that time, her children had moved out, but still visited frequently, and brought their girlfriends, so we weren't so distant from them either. And I spent long portions of off-time at my grandparents' home, during the summer and winter.
Nowadays, with extended family ties being moderately strong at best, generational membership is going to be primarily shaped by your own birth year, period. That determines who your peers will be in school, and there's your generation. But that still leaves secondary influence for the generational make-up of your extended family, and in cases where you belong to a cohort that is neither here nor there, this secondary influence could push you clearly into one or the other clearly defined generation on either side of your own.